Estimation of unbiased delays

A large number of exploration processing procedures need the solution to the problem stated as, "Given a set of seismic traces, determine the common element." This element could be the seismic wavelet, as in a set of common-shot traces or as in a set of stack traces that need to be matched with synthetic seismograms. It could also be a pilot trace representing a noise-foe estimate of traces in a common-depth-point (CDP) gather to be used during an automatic time and phase statics computation. Most present computations use iteratively improved estimates of one sort or another. They assume that initial estimates are close enough to ensure that subsequent steps will produce more accurate results. The problem. of course, is the accuracy of the first unbiased estimation: when it fails, the rest becomes uncertain. In this paper we introduce a method that provides a robust solution to the problem of finding the common element. We also show that the method may be used to estimate both common wavelets and pilot traces conveniently with error correction facilities.